The ambient homeomorphy of certain function and sequence spaces
Dijkstra, Jan J. ; Mogilski, Jerzy
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996), p. 595-611 / Harvested from Czech Digital Mathematics Library
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In this paper we consider a number of sequence and function spaces that are known to be homeomorphic to the countable product of the linear space $\sigma$. The spaces we are interested in have a canonical imbedding in both a topological Hilbert space and a Hilbert cube. It turns out that when we consider these spaces as subsets of a Hilbert cube then there is only one topological type. For imbeddings in the countable product of lines there are two types depending on whether the space is contained in a $\sigma$-compactum or not.

Publié le : 1996-01-01
Classification:  54C35,  57N17,  57N20 
@article{118866,
     author = {Jan J. Dijkstra and Jerzy Mogilski},
     title = {The ambient homeomorphy of certain function and sequence spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {37},
     year = {1996},
     pages = {595-611},
     zbl = {0881.57018},
     mrnumber = {1426924},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118866}
}

Dijkstra, Jan J.; Mogilski, Jerzy. The ambient homeomorphy of certain function and sequence spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) pp. 595-611. http://gdmltest.u-ga.fr/item/118866/

Baars J.; Gladdines H.; Van Mill J. Absorbing systems in infinite-dimensional manifolds, Topology Appl. 50 (1993), 147-182. (1993) | MR 1217483 | Zbl 0794.57005

Bessaga C.; Pełczyński A. Selected Topics in Infinite-Dimensional Topology, PWN Warsaw (1975). (1975)

Curtis D.W. Boundary sets in the Hilbert cube, Topology Appl. 20 (1985), 201-221. (1985) | MR 0804034 | Zbl 0575.57008

Dijkstra J.J.; Dobrowolski T.; Marciszewski W.; Van Mill J.; Mogilski J. Recent classification and characterization results in geometric topology, Bull. Amer. Math. Soc. 22 (1990), 277-283. (1990) | MR 1027899 | Zbl 0713.57011

Dijkstra J.J.; Van Mill J.; Mogilski J. The space of infinite-dimensional compacta and other topological copies of $(l^2_{an f})^ømega$, Pacific. J. Math. 152 (1992), 255-273. (1992) | MR 1141795

Dijkstra J.J.; Mogilski J. The topological product structure of systems of Lebesgue spaces, Math. Ann. 290 (1991), 527-543. (1991) | MR 1116236 | Zbl 0734.46013

Dobrowolski T.; Marciszewski W.; Mogilski J. On topological classification of function spaces $C_{an p}(X)$ of low Borel complexity, Trans. Amer. Math. Soc. 328 (1991), 307-324. (1991) | MR 1065602

Dobrowolski T.; Mogilski J. Problems on topological classification of incomplete metric spaces, 409-429 in Open Problems in Topology, J. van Mill and G.M. Reed, eds., North-Holland, Amsterdam, 1990. | MR 1078661

Dobrowolski T.; Mogilski J. Certain sequence and function spaces homeomorphic to the countable product of $l_f^2$, J. London Math. Soc. 45.2 (1992), 566-576. (1992) | MR 1180263

Lutzer D.; Mccoy R. Category in function spaces I, Pacific J. Math. 90 (1980), 145-168. (1980) | MR 0599327 | Zbl 0481.54017

Van Mill J. Topological equivalence of certain function spaces, Compositio Math. 63 (1987), 159-188. (1987) | MR 0906368 | Zbl 0634.54011

Van Mill J. Infinite-Dimensional Topology, Prerequisites and Introduction, North-Holland Amsterdam (1989). (1989) | MR 0977744 | Zbl 0663.57001